Don't use current user's email by default on job submission.
// Add your own function to filter the fields
add_filter( 'submit_job_form_fields_get_user_data', 'custom_submit_job_form_fields' );
// This is your function which takes the fields, modifies them, and returns them
// You can see the fields which can be changed here: https://github.com/mikejolley/WP-Job-Manager/blob/master/includes/forms/class-wp-job-manager-form-submit-job.php
function custom_submit_job_form_fields( $fields ) {
// Here we target one of the job fields (job_title) and change it's label
$fields['job']['application']['value'] = 'Enter an email address';
// And return the modified fields
return $fields;
}